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Metaheuristic optimization algorithms (MHA) play a significant role in obtaining the best (optimal) values of the system's parameters to improve its performance. This role is significantly apparent when dealing with systems where the classical analytical methods fail. Fractional-order (FO) systems have not yet shown an easy procedure to deal with the determination of their optimal parameters through traditional methods. In this paper, a recent, systematic. And comprehensive review is presented to highlight the role of MHA in obtaining the best set of gains and orders for FO controllers. The systematic review starts by exploring the most relevant publications related to the MHA and the FO controllers. The study is focused on the most popular controllers such as the FO-PI, FO-PID, FO Type-1 fuzzy-PID, and FO Type-2 fuzzy-PID. The time domain is restricted in the articles published through the last decade (2014:2023) in the most reputed databases such as Scopus, Web of Science, Science Direct, and Google Scholar. The identified number of papers, from the entire databases, has reached 850 articles. A Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) methodology was applied to the initial set of articles to be screened and filtered to end up with a final list that contains 82 articles. Then, a thorough and comprehensive study was applied to the final list. The results showed that Particle Swarm Optimization (PSO) is the most attractive optimizer to the researchers to be used in the optimal parameters identification of the FO controllers as it attains about 25% of the published papers. In addition, the papers that used PSO as an optimizer have gained a high citation number despite the fact that the Chaotic Atom Search Optimization (ChASO) is the highest one, but it is used only once. Furthermore, the Integral of the Time-Weighted Absolute Error (ITAE) is the best nominated cost function. Based on our comprehensive literature review, this appears to be the first review paper that systematically and comprehensively addresses the optimization of the parameters of the fractional-order PI, PID, Type-1, and Type-2 fuzzy controllers with the use of MHAs. Therefore, the work in this paper can be used as a guide for researchers who are interested in working in this field. [ABSTRACT FROM AUTHOR]

This paper introduces a new variant of the Bees Algorithm (BA) called Bees Algorithm with 2-parameter (BA2), which is a population-based metaheuristic algorithm designed to solve continuous and combinatorial optimisation problems. The proposed algorithm simplified the BA's parameters by combining exploration and exploitation strategies while preserving the algorithm's core principles to efficiently search for optimal solutions. The paper provides a detailed description of the algorithm's core principles and its application to two engineering problems, the air-cooling system design (ACSD) and the printed circuit board assembly sequence optimisation (PASO). The results show that BA2 outperforms previous versions of the basic BA in terms of convergence speed and solution quality. However, the authors acknowledge that further research is needed to test the scalability and generalisability of the algorithm to larger and more diverse optimisation problems. Overall, this paper provides valuable insights into the potential of metaheuristics for solving real-world optimisation problems. [ABSTRACT FROM AUTHOR]

The capacitated dispersion problem, which is a variant of the maximum diversity problem, aims to determine a set of elements within a network. These elements could symbolize, for instance, facilities in a supply chain or transmission nodes in a telecommunication network. While each element typically has a bounded service capacity, in this research, we introduce a twist. The capacity of each node might be influenced by a random Bernoulli component, thereby rendering the possibility of a node having zero capacity, which is contingent upon a black box mechanism that accounts for environmental variables. Recognizing the inherent complexity and the NP-hard nature of the capacitated dispersion problem, heuristic algorithms have become indispensable for handling larger instances. In this paper, we introduce a novel approach by hybridizing a heuristic algorithm with reinforcement learning to address this intricate problem variant. [ABSTRACT FROM AUTHOR]

This paper introduces an evolutionary algorithm for n-dimensional single objective optimization problems: One-Dimensional Subspaces Optimization Algorithm (1D-SOA). The algorithm starts with an initial population in randomly selected positions. For each individual, a percentage of the total number of dimensions is selected, each dimension corresponding to a one-dimensional subspace. Later, it performs a symmetric search for the nearest local optima in all the selected one-dimensional subspaces (1D-S), for each individual at a time. The search stops if the new position does not improve the value of the objective function over all the selected 1D-S. The performance of the algorithm was compared against 11 algorithms and tested with 30 benchmark functions in 2 dimensions (D) and 30D. The proposed algorithm showed a better performance than all other studied algorithms for large dimensions. [ABSTRACT FROM AUTHOR]

The university course timetable problem (UCTP) is known to be NP-hard, with solution complexity growing exponentially with the problem size. This paper introduces an algorithm that effectively tackles UCTPs by employing a combination of exploration and exploitation strategies. The algorithm comprises two main components. Firstly, it utilizes a genetic algorithm (GA) to explore the search space and discover a solution within the global optimum region. Secondly, it enhances the solution by exploiting the region using an iterated local search (ILS) algorithm. The algorithm is tested on two common variants of UCTP: the post-enrollment-based course timetable problem (PE-CTP) and the curriculum-based course timetable problem (CB-CTP). The computational results demonstrate that the proposed algorithm yields competitive outcomes when compared empirically against other existing algorithms. Furthermore, a t-test comparison with state-of-the-art algorithms is conducted. The experimental findings also highlight that the hybrid approach effectively overcomes the limitation of local optima, which is encountered when solely employing GA in conjunction with local search. [ABSTRACT FROM AUTHOR]

Swarm Intelligence (SI) algorithms are frequently applied to tackle complex optimization problems. SI is especially used when good solutions are requested for NP hard problems within a reasonable response time. And when such problems possess a very high dimensionality, a dynamic nature, or present intrinsic complex intertwined independent variables, computational costs for SI algorithms may still be too high. Therefore, new approaches and hardware support are needed to speed up processing. Nowadays, with the popularization of GPU and multi-core processing, parallel versions of SI algorithms can provide the required performance on those though problems. This paper aims to describe the state of the art of such approaches, to summarize the key points addressed, and also to identify the research gaps that could be addressed better. The scope of this review considers recent papers mainly focusing on parallel implementations of the most frequently used SI algorithms. The use of nested parallelism is of particular interest, since one level of parallelism is often not sufficient to exploit the computational power of contemporary parallel hardware. The sources were main scientific databases and filtered accordingly to the set requirements of this literature review. [ABSTRACT FROM AUTHOR]

Academic institutions may be edging towards a global uncertainty, recession, and a string of financial difficulties. An effective course timetabling is one of managerial strategies to optimise the operating costs and resource utilisation. This paper presents the first application of firefly algorithm (FA) and its modifications and hybridisations for solving real-world course timetabling problem. A novel bi-objective firefly algorithm (BOFA) with Pareto dominance approach was developed for optimising the operating costs and resource utilisation. Random key technique was applied for adapting the continuous firefly movement to solve discrete timetabling problem. Five constructive heuristics were additionally embedded into the BOFA for initialising feasible timetables. Computational experiments were sequentially conducted using eleven problem instances obtained from a collaborating university. It was found that the proposed hybridisation outperformed particle swarm optimisation, the classical FA, and modified FA (MFA), in terms of the quality of the timetables obtained, computational times and convergent speed. The proposed hybrid bi-objective FA (HBOFA) yielded better Pareto frontiers than the conventional BOFA with less computational times for all problem instances. [ABSTRACT FROM AUTHOR]

In recent years, metaheuristic methods have shown remarkable efficacy in resolving complex combinatorial challenges across a broad spectrum of fields. Nevertheless, the escalating complexity of these problems necessitates the continuous development of innovative techniques to enhance the performance and reliability of these methods. This paper aims to contribute to this endeavor by examining the impact of solution initialization methods on the performance of a hybrid algorithm applied to the set union knapsack problem (SUKP). Three distinct solution initialization methods, random, greedy, and weighted, have been proposed and evaluated. These have been integrated within a sine cosine algorithm employing k-means as a binarization procedure. Through testing on medium- and large-sized SUKP instances, the study reveals that the solution initialization strategy influences the algorithm's performance, with the weighted method consistently outperforming the other two. Additionally, the obtained results were benchmarked against various metaheuristics that have previously solved SUKP, showing favorable performance in this comparison. [ABSTRACT FROM AUTHOR]

The search for a better approach to design a convenient controlling scheme is one of the main challenges of the research field related to power converters. This paper brings forward a significant contribution as part of this challenge. In this regard, novel approaches have been proposed for both controller scheme and tuning algorithm. In terms of controlling scheme, a fractional-order proportional–integral–derivative (FOPID) controller was used alongside the Bode's ideal transfer function to achieve optimum performance of a buck converter system. To achieve a greater performance of the FOPID controller, a novel metaheuristic algorithm, which consists of a balanced structure in terms of explorative and exploitative phases, has also been developed by hybridizing the hunger games search algorithm with simulated annealing technique. The proposed hybrid algorithm helped tuning the FOPID controller optimally. The proposed algorithm and controlling scheme have been proved to be a better approach for controlling a buck converter system in terms of time and frequency domains along with disturbance rejection. To further verify the effectiveness of the proposed hybrid algorithm–based controlling scheme, it was compared with other reported and capable approaches which have also confirmed the greater performance of the proposed approach. [ABSTRACT FROM AUTHOR]

Metaheuristics are algorithms that are used to solve difficult optimization problems. They are typically stochastic approaches; hence, proper statistical tests are needed to compare them. However, choosing an appropriate statistical test is not trivial given that each test requires some assumptions to be true before the test can be used. Moreover, the p-values associated with a statistical test is usually difficult to interpret. In this paper, we propose the use of Laplace's rule of succession to compare different metaheuristic approaches. The rule is simple, intuitive and easy to compute. It can be used alone or to complement a statistical test. The process of using the rule for comparison purposes is clearly explained and applied to a typical scenario encountered in the field of metaheuristics. In this scenario, an improved variant of an existing metaheuristic algorithm is proposed. To evaluate the performance of the two algorithms, Laplace's rule and a traditional statistical test are used. Analysis of the results and how to interpret them are provided. The results show that Laplace's rule is consistent with the used statistical test. Furthermore, the rule is easier to compute and interpret. [ABSTRACT FROM AUTHOR]

Electric vehicle production is subjected to high manufacturing cost and environmental impact. Disassembling and remanufacturing the lithium-ion power packs can highly promote electric vehicle market penetration by procuring and regrouping reusable modules as stationary energy storage devices and cut life-cycle cost and environmental impact. Disassembly efficiency is crucial for battery remanufacturing companies in reverse supply chains. However, disassembly planning suffers from high computational complexity and inferior solutions. This paper developed a multi-objective mathematical model and presented a novel hybrid genetic-firework algorithm based on the precedence graph for obtaining solutions to disassemble the electric vehicle power pack into module levels in an efficient manner. The objectives for the model include not only smoothness of working stations, cycle time, and economic returns, but also consider operation safety and energy consumption. The proposed hybrid algorithm explored the performance of the novel solution searching mechanism of combining the firework and genetic algorithms. The proposed approach is compared with the commonly used multi-objective evolutionary algorithms in the literature, showing its feasibility and effectiveness. [ABSTRACT FROM AUTHOR]

Multi‐objective optimization problems frequently appear in many diverse research areas and application domains. Metaheuristics, as efficient techniques to solve them, need to be easily accessible to users with different expertise and programming skills. In this context, metaheuristic optimization frameworks are helpful, as they provide popular algorithms, customizable components and additional facilities to conduct experiments. Due to the broad range of available tools, this paper presents a systematic evaluation and experimental comparison of 10 frameworks, covering from multi‐purpose, consolidated tools to recent libraries specifically designed for multi‐objective optimization. The evaluation is organized around seven characteristics: search components and techniques, configuration, execution, utilities, external support and community, software implementation and performance. An analysis of code metrics and a series of experiments serves to assess the last two features. Lesson learned and open issues are also discussed as part of the comparative study. The outcomes of the evaluation process reveal a contrasted support to recent advances in multi‐objective optimization, with a lack of novel algorithms and variety of metaheuristics other than evolutionary algorithms. The experimental comparison also reports significant differences in terms of both execution time and memory usage under demanding configurations. [ABSTRACT FROM AUTHOR]

Intrusion detection systems (IDS) play a crucial role in securing networks and identifying malicious activity. This is a critical problem in cyber security. In recent years, metaheuristic optimization algorithms and deep learning techniques have been applied to IDS to improve their accuracy and efficiency. Generally, optimization algorithms can be used to boost the performance of IDS models. Deep learning methods, such as convolutional neural networks, have also been used to improve the ability of IDS to detect and classify intrusions. In this paper, we propose a new IDS model based on the combination of deep learning and optimization methods. First, a feature extraction method based on CNNs is developed. Then, a new feature selection method is used based on a modified version of Growth Optimizer (GO), called MGO. We use the Whale Optimization Algorithm (WOA) to boost the search process of the GO. Extensive evaluation and comparisons have been conducted to assess the quality of the suggested method using public datasets of cloud and Internet of Things (IoT) environments. The applied techniques have shown promising results in identifying previously unknown attacks with high accuracy rates. The MGO performed better than several previous methods in all experimental comparisons. [ABSTRACT FROM AUTHOR]

This paper presents a population-based evolutionary computation model for solving continuous constrained nonlinear optimization problems. The primary goal is achieving better solutions in a specific problem type, regardless of metaphors and similarities. The proposed algorithm assumes that candidate solutions interact with each other to have better fitness values. The interaction between candidate solutions is limited with the closest neighbors by considering the Euclidean distance. Furthermore, Tabu Search Algorithm and Elitism selection approach inspire the memory usage of the proposed algorithm. Besides, this algorithm is structured on the principle of the multiplicative penalty approach that considers satisfaction rates, the total deviations of constraints, and the objective function value to handle continuous constrained problems very well. The performance of the algorithm is evaluated with real-world engineering design optimization benchmark problems that belong to the most used cases by evolutionary optimization researchers. Experimental results show that the proposed algorithm produces satisfactory results compared to the other algorithms published in the literature. The primary purpose of this study is to provide an algorithm that reaches the best-known solution values rather than duplicating existing algorithms through a new metaphor. We constructed the proposed algorithm with the best combination of features to achieve better solutions. Different from similar algorithms, constrained engineering problems are handled in this study. Thus, it aims to prove that the proposed algorithm gives better results than similar algorithms and other algorithms developed in the literature. [ABSTRACT FROM AUTHOR]

The efficiency and the effectiveness of a machine learning (ML) model are greatly influenced by feature selection (FS), a crucial preprocessing step in machine learning that seeks out the ideal set of characteristics with the maximum accuracy possible. Due to their dominance over traditional optimization techniques, researchers are concentrating on a variety of metaheuristic (or evolutionary) algorithms and trying to suggest cutting-edge hybrid techniques to handle FS issues. The use of hybrid metaheuristic approaches for FS has thus been the subject of numerous research works. The purpose of this paper is to critically assess the existing hybrid FS approaches and to give a thorough literature review on the hybridization of different metaheuristic/evolutionary strategies that have been employed for supporting FS. This article reviews pertinent documents on hybrid frameworks that were published in the period from 2009 to 2022 and offers a thorough analysis of the used techniques, classifiers, datasets, applications, assessment metrics, and schemes of hybridization. Additionally, new open research issues and challenges are identified to pinpoint the areas that have to be further explored for additional study. [ABSTRACT FROM AUTHOR]

In this paper, we study the quadratic assignment problem with a rank-one cost matrix (QAP-R1). Four integer-programming formulations are introduced of which three are assumed to have partial integer data. Unlike the standard quadratic assignment problem, some of our formulations can solve reasonably large instances of QAP-R1 with impressive running times and are faster than some metaheuristics. Pairwise relative strength of the LP relaxations of these formulations are also analyzed from theoretical and experimental points of view. Finally, we present a new metaheuristic algorithm to solve QAP-R1 along with its computational analysis. Our study offers the first systematic experimental analysis of integer-programming models and heuristics for QAP-R1. The benchmark instances with various characteristics generated for our study are made available to the public for future research work. Some new polynomially solvable special cases are also introduced. Summary of Contribution: This paper aims to advance our knowledge and ability in solving an important special case of the quadratic assignment problem. It shows how to exploit inherent properties of an optimization problem to achieve computational advantages, a strategy that was followed by researchers in model building and algorithm developments for decades. Our computational results attest to this time-tested general philosophy. The paper presents the first systematic computational study of the rank one quadratic assignment problem, along with new mathematical programming models and complexity analysis. We believe the theoretical and computational results of this paper will inspire further research on the topic and will be of significant value to practitioners using rank one quadratic assignment models. [ABSTRACT FROM AUTHOR]

Bat-inspired algorithm (BA) is a robust swarm intelligence algorithm that finds success in many problem domains. The ecosystem of bat animals inspires the main idea of BA. This review paper scanned and analysed the state-of-the-art researches investigated using BA from 2017 to 2021. BA has very impressive characteristics such as its easy-to-use, simple in concepts, flexible and adaptable, consistent, and sound and complete. It has strong operators that incorporate the natural selection principle through survival-of-the-fittest rule within the intensification step attracted by local-best solution. Initially, the growth of the recent solid works published in Scopus indexed articles is summarized in terms of the number of BA-based Journal articles published per year, citations, top authors, work with BA, top institutions, and top countries. After that, the different versions of BA are highlighted to be in line with the complex nature of optimization problems such as binary, modified, hybridized, and multiobjective BA. The successful applications of BA are reviewed and summarized, such as electrical and power system, wireless and network system, environment and materials engineering, classification and clustering, structural and mechanical engineering, feature selection, image and signal processing, robotics, medical and healthcare, scheduling domain, and many others. The critical analysis of the limitations and shortcomings of BA is also mentioned. The open-source codes of BA code are given to build a wealthy BA review. Finally, the BA review is concluded, and the possible future directions for upcoming developments are suggested such as utilizing BA to serve in dynamic, robust, multiobjective, large-scaled optimization as well as improve BA performance by utilizing structure population, tuning parameters, memetic strategy, and selection mechanisms. The reader of this review will determine the best domains and applications used by BA and can justify their BA-related contributions. [ABSTRACT FROM AUTHOR]

Optimization problems are prevalent in almost all areas and hence optimization algorithms are crucial for a myriad of real-world applications. Deterministic optimization algorithms tend to be computationally costly and time-consuming. Hence, heuristic and metaheuristic algorithms are more favoured as they provide near-optimal solutions in an acceptable amount of time. Swarm intelligence algorithms are being increasingly used for optimization problems owing to their simplicity and good performance. The Dragonfly Algorithm (DA) is one which is inspired by the swarming behaviours of dragonflies, and it has been proven to have a superior performance than other algorithms in multiple applications. Hence, it is worth considering its application to the traveling salesman problem which is a predominant discrete optimization problem. The original DA is only suitable for solving continuous optimization problems and, although there is a binary version of the algorithm, it is not easily adapted for solving discrete optimization problems like TSP. We have previously proposed a discrete adapted DA algorithm suitable for TSP. However, it has low effectiveness, and it has not been used for large TSP problems. In this paper, we propose an optimized discrete adapted DA by using the steepest ascent hill climbing algorithm as a local search. The algorithm is applied to a TSP problem modelling a package delivery system in the Kuala Lumpur area and to benchmark TSP problems, and it is found to have a higher effectiveness than the discrete adapted DA and some other swarm intelligence algorithms. It also has a higher efficiency than the discrete adapted DA. [ABSTRACT FROM AUTHOR]

Optimization is a very important issue to efficiently solve engineering problems. The clear comprehension of the elements and processes of optimizer algorithms is fundamental to ensure that engineer students are capable to apply, tune, and design new algorithms. This paper presents an educational platform based on LEGO© EV3 and MATLAB to assist the learning of the principles of classical and metaheuristic optimization algorithms at undergraduate level, by providing a simple and easy-to-follow teaching setup. The proposed study aims to accompany students through the learning of optimization fundamentals by building hands-on robotic experiments. The proposed educational platform has been successfully applied to several undergraduate courses within the Electronics Department at the University of Guadalajara. The description of each experiment and the evaluation of their impact in the student performance are both provided in the paper. [ABSTRACT FROM AUTHOR]

Finding the conditions under which packing algorithms succeed or fail with respect to a set of test instances is crucial for understanding their strengths and weaknesses, and for automated packing algorithm selection. This paper tackles the important task of objective packing algorithm selection. A framework for understanding the relationship between critical features of packing problem instances and the performance of packing algorithms is proposed. The framework can be used to predict algorithm performance on previously unseen instances with high accuracy and can be applied to find predictions in other instances of cutting and packing problems. It can also be applied to determine the relative strengths and weaknesses of each algorithm within the instance space. The effectiveness of the framework is demonstrated using the two-dimensional strip packing problem as a case study. [ABSTRACT FROM AUTHOR]

Many metaheuristic approaches are inherently stochastic. In order to compare such methods, statistical tests are needed. However, choosing an appropriate test is not trivial, given that each test has some assumptions about the distribution of the underlying data that must be true before it can be used. Permutation tests (P-Tests) are statistical tests with minimal number of assumptions. These tests are simple, intuitive and nonparametric. In this paper, we argue researchers in the field of metaheuristics to adopt P-Tests to compare their algorithms. We define two statistic tests and then present an algorithm that uses them to compute the p-value. The proposed process is used to compare 5 metaheuristic algorithms on 10 benchmark functions. The resulting p-values are compared with the p-values of two widely used statistical tests. The results show that the proposed P-test is generally consistent with the classical tests, but more conservative in few cases. [ABSTRACT FROM AUTHOR]

This paper presents a novel metaheuristic optimization algorithm inspired by the geometrical features of circles, called the circle search algorithm (CSA). The circle is the most well-known geometric object, with various features including diameter, center, perimeter, and tangent lines. The ratio between the radius and the tangent line segment is the orthogonal function of the angle opposite to the orthogonal radius. This angle plays an important role in the exploration and exploitation behavior of the CSA. To evaluate the robustness of the CSA in comparison to other algorithms, many independent experiments employing 23 famous functions and 3 real engineering problems were carried out. The statistical results revealed that the CSA succeeded in achieving the minimum fitness values for 21 out of the tested 23 functions, and the p-value was less than 0.05. The results evidence that the CSA converged to the minimum results faster than the comparative algorithms. Furthermore, high-dimensional functions were used to assess the CSA's robustness, with statistical results revealing that the CSA is robust to high-dimensional problems. As a result, the proposed CSA is a promising algorithm that can be used to easily handle a wide range of optimization problems. [ABSTRACT FROM AUTHOR]

In recent years, significant attentions have been devoted to design of metaheuristic optimization algorithms in order to solve optimization problems. Metaheuristic optimizers are methods which are inspired by observing the phenomena occurring in nature. In this paper, a comprehensive and exhaustive review has been carried out on water cycle algorithm (WCA) and its applications in a wide variety of study fields. The WCA is one of the novel metaheuristic optimization algorithms which is inspired by water cycle process in nature and how streams and rivers flow into the sea. Good exploitation and exploration capabilities have made the WCA a good alternative for solving large-scale optimization problems. Due to its capabilities and strengths, the WCA has been utilized in many and various majors including mechanical engineering, electrical and electronic engineering, civil engineering, industrial engineering, water resources and hydropower engineering, computer engineering, mathematics, and so forth. A variety of articles based on WCA have been published in different international journals such as Elsevier, Springer, IEEE Transactions, Wiley, Taylor & Francis, and in the proceedings of international conferences as well, since 2012 to the present. Thus, it is highly believed that this paper can be appropriate, beneficial and practical for students, academic researchers, professionals, and engineers. Also, it can be an innovative and comprehensive reference for subsequent academic papers and books relevant to the WCA, optimization methods, and metaheuristic optimization algorithms. [ABSTRACT FROM AUTHOR]

Recent growth of metaheuristic search strategies has brought a huge progress in the domain of computational optimization. The breakthrough started since the well-known Particle Swarm Optimization algorithm had been introduced and examined. Optimization technique presented in this contribution mimics the process of flower pollination. It is build on the foundation of the first technique of this kind—known as Flower Pollination Algorithm (FPA). In this paper, its simplified and improved version, obtained after extensive performance testing, is presented. It is based on only one natural phenomena—called flower constancy—the natural mechanism allowing pollen carrying insects to remember the positions of the best pollen sources. Modified FPA, named as Biotic Flower Pollination Algorithm (BFPA) and relying solely on biotic pollinators, outperforms original FPA, which itself proved to be very effective approach. The paper first presents a short description of original FPA and the changes leading to Biotic Flower Pollination Algorithm. It also discusses performance of the modified algorithm on a full set of CEC17 benchmark functions. Furthermore, in that aspect, the comparison between BFPA and other optimization algorithms is also given. Finally, brief exemplary application of modified algorithm in the field of probabilistic modeling, related to physics and engineering, is also presented. [ABSTRACT FROM AUTHOR]

The main goal of this paper is to outline a new approach to represent the randomness that we can find in different metaheuristics as a stochastic process which helps in the performance of the analyzed metaheuristic. This new way of viewing randomness is based on the behavior of sine waves that we can find in many situations in nature or in physics laws. In this paper, we evaluate this proposed randomness with three metaheuristics: the grey wolf optimizer, firefly algorithm and flower pollination algorithm, with the goal of studying the performance of the proposed randomness method in different types of metaheuristics. A set of standard benchmark functions were used to test the proposed randomness method, which are classified as unimodal and multimodal benchmark functions. In addition, the benchmark functions of the CEC 2015 Competition are used. Finally, we present tests with functions that were presented in the CEC 2017 competition for constrained real-parameter optimization. We also present a comparative study of the analyzed metaheuristics, and this comparison is between their original randomness method and the proposed randomness method for each algorithm. Finally, we present the performance and results of the methods with different number of dimensions to complete the study. [ABSTRACT FROM AUTHOR]

Data analysis becomes more important since rapid technology developments. In data analysis, data clustering is one of the very useful approaches. It can reveal important information hiding inside the dataset by organizing the instances based on their similarity. The objectives of data clustering are maximizing dissimilarity between clusters and minimizing dissimilarity within clusters. In order to construct a good clustering results, many clustering algorithms have been proposed, including the metaheuristic-based clustering algorithms. Recently, a new metaheuristic algorithm named gradient evolution has been proposed. This algorithm shows a good performance on solving the optimization problems. Therefore, this paper employs this GE algorithm for solving the clustering problem. In order to obtain a better clustering result, this paper considers multi-objective clustering instead of single-objective clustering. In this paper, the original GE algorithm is improved so then it is suitable for the multi-objective problem. The proposed modification includes the procedure for vector updating and jumping which involves Pareto rank assignment. In addition, it also employs K-means algorithm to provide the final clustering result. The proposed algorithm is verified using some benchmark datasets. It is also compared with some other multi-objective metaheuristic-based clustering algorithms. The experimental results show that the proposed algorithm can obtain better results than other metaheuristic-based algorithms. [ABSTRACT FROM AUTHOR]

Parameter-free algorithms are of an increasing interest in applications that require out-of-the-box solving techniques. For instance, scheduling in volatile environments or control parameters optimisation often requires flexible solving approaches without the need to tune or retune the parameters. In addition, parameter-free algorithms are usually beneficial in solving previously unexplored real-world problem instances. In this paper, we propose a parameter-free local search strategy to solve graph colouring, which is the underlying problem for a number of scheduling applications. Two variants of parameter-free local search are computationally investigated: PFLS-A and PFLS-B. Both of these algorithms are based on accepting strictly improving moves and operating as a random walk if no strictly improving move is found. PFLS-A and PFLS-B differ in randomised versus systematic exploration of the neighbourhood of the current solution. Their cooperative variant CPFLS is also proposed. We compare the results of these three algorithms to the results obtained by 13 other local search methods from the literature. CPFLS provides better or equal results as the other local search algorithms in 67.25 % of per-instance comparisons. This is without employing any explicit or implicit parameters that are usually used in metaheuristics. This hints the promising nature of parameter-free metaheuristics not only for this problem but also metaheuristics in general. [ABSTRACT FROM AUTHOR]

Grey Wolf Optimizer (GWO) is a nature-inspired swarm intelligence algorithm that mimics the hunting behavior of grey wolves. GWO, in its basic form, is a real coded algorithm that needs modifications to deal with binary optimization problems. In this paper, previous work on the binarization of GWO are reviewed, and are classified with respect to their encoding scheme, updating strategy, and transfer function. Then, we propose a novel binary GWO algorithm (named SetGWO), which is based on set encoding and uses set operations in its updating strategy. The proposed algorithm uses a completely different encoding scheme that eliminates the need for the transfer function and boundary checking, and also uses lower-dimensional agents; therefore, decreases the running time. Also, by using an exclusive exploration set for each agent, defining a different distance measure and an encircling strategy in discrete spaces, the quality of solutions has been improved. Experimental results on different real-world combinatorial optimization problems and datasets show that SetGWO outperforms other existing binary GWO algorithms in terms of quality of solutions, running time, and scalability. [ABSTRACT FROM AUTHOR]

This paper presents a powerful swarm intelligence metaheuristic optimization algorithm called Dynamic Cat Swarm Optimization. The formulation is through modifying the existing Cat Swarm Optimization Algorithm. The original Cat Swarm Optimization suffers from the shortcoming of "premature convergence," which is the possibility of entrapment in local optima which usually happens due to the off balance between exploration and exploitation phases. Therefore, the proposed algorithm suggests a new method to provide a proper balance between these phases by modifying the selection scheme and the seeking mode of the algorithm. To evaluate the performance of the proposed algorithm, 23 classical test functions, 10 modern test functions (CEC 2019) and a real-world scenario are used. In addition, the dimension-wise diversity metric is used to measure the percentage of the exploration and exploitation phases. The optimization results show the effectiveness of the proposed algorithm, which ranks first compared to several well-known algorithms available in the literature. Furthermore, statistical methods and graphs are also used to further confirm the outperformance of the algorithm. Finally, the conclusion and future directions to further improve the algorithm are discussed. [ABSTRACT FROM AUTHOR]

The present paper deals with structural health monitoring of trusses, space frame and plate structure utilizing the Bayesian data fusion approach. The application of the proposed approach has been demonstrated on a 25-member plane truss, a 42-member space frame, a cantilever plate and a 120-member space truss. Different damage indexes of interest have been calculated for the damaged structure utilizing the natural frequency and modeshapes as damage indicators. Damage indexes used are modal strain energy (DIMSE), frequency response function strain energy dissipation ratio (FRFSEDR), flexibility strain energy damage ratio (FSEDR) and residual force-based damage index (RFBDI). Next, the Bayesian data fusion approach has been applied to these four damage indexes to find out the accurate damage location. The proposed approach reduces the number of suspected damaged elements in the structure significantly, thus reducing the computational time of optimization algorithm. Proposed algorithm has also shown encouraging performance in noisy environments. Overall present approach is found to be robust and computationally efficient, and thus can be applied for damage detection involving field evaluation of various structures. [ABSTRACT FROM AUTHOR]

This paper describes a proposed competitive multi-metaheuristic optimization model for the optimal design of membership function parameters of a fuzzy system that controls the navigation of an autonomous mobile robot following a desired trajectory. The main contribution is the new competitive multi-metaheuristic optimization model, which is formed by an architecture consisting of the firefly algorithm, wind-driven optimization, drone squadron optimization, and stochastic fractal search. The proposed method has enable obtaining good results in the optimization of fuzzy controllers, which outperform other metaheuristics in the literature. In the competition, each of the methods is tested until finding the best one in generating an effective parameter vector for the optimization of fuzzy controller membership functions. The main contribution of this article is the use of four metaheuristics working in a competitive way, to find the best vector of data generated with the optimal values to successfully adjust the membership functions of the fuzzy controller. The resulting winning method proves in this way that it is the best among the chosen algorithms to solve this kind of control optimization problem. [ABSTRACT FROM AUTHOR]

A novel nature-inspired metaheuristic optimization algorithm, called the quantum firefly algorithm, is proposed in this paper. The algorithm imitates (a) the social behaviour of fireflies mating in nature, (b) laws of quantum physics, and (c) laws of natural evolution. The algorithm combines the powers of two well-known algorithms: the firefly algorithm and the quantum genetic algorithm. The proposed quantum firefly algorithm's performance is tested on 15 mathematical test functions and one structural design problem. The obtained results show that the quantum firefly algorithm is very competitive compared to the firefly algorithm and the quantum genetic algorithm. [ABSTRACT FROM AUTHOR]

Feature transformation methods can be used effectively to improve the performance of the machine learning techniques, such as classification and clustering, via enhancing the discrimination among the samples. Additionally, binary representation of features may be necessary in several circumstances. For example, distributed systems may have limited bandwidth, storage, and energy that necessitate rough quantization of the measurements. This paper proposes a random projection-based feature transformation method that maps the data points from the original space into a new binary space. In the proposed transformation method, the random projection process is formulated as an optimization problem. A modified chaotic version of the sine–cosine algorithm is used to find the optimal random projector. The performance of the proposed transformation method is validated using 15 standard UCI benchmark datasets against the linear discernment analysis. Moreover, it is compared to other metaheuristic-based feature reduction methods including the gray wolf optimizer, the genetic algorithm, and the antlion optimizer. The obtained results assure the superiority of the proposed transformation method in terms of classification accuracy and storage requirements. [ABSTRACT FROM AUTHOR]

In this paper, improved salp swarm algorithm is proposed. The algorithm integrates (1) random opposition-based learning (2) multiple leadership and (3) simulated annealing in swarm intelligence-based metaheuristic salp swarm algorithm. This integration increases the exploration and exploitation of the original salp swarm algorithm. Hence, the effectiveness of the proposed algorithm is better for complex multi-modal problems. The algorithm is tested on several standard numerical benchmark functions and CEC-2015 benchmarks. Results are compared with some well-known metaheuristics. The results represent the merit of the proposed algorithm with respect to other algorithms. The improved salp swarm algorithm is applied for feed-forward neural network training. Performance is compared with other metaheuristic-based feedforward neural network trainers for different data sets. The results show the efficiency and effectiveness of proposed algorithm in solving complex multi-modal problems. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast and scalable, yet effective, metaheuristic called FILO to solve large-scale instances of the Capacitated Vehicle Routing Problem. Our approach consists of a main iterative part, based on the Iterated Local Search paradigm, which employs a carefully designed combination of existing acceleration techniques, as well as novel strategies to keep the optimization localized, controlled, and tailored to the current instance and solution. A Simulated Annealing-based neighbor acceptance criterion is used to obtain a continuous diversification, to ensure the exploration of different regions of the search space. Results on extensively studied benchmark instances from the literature, supported by a thorough analysis of the algorithm's main components, show the effectiveness of the proposed design choices, making FILO highly competitive with existing state-of-the-art algorithms, both in terms of computing time and solution quality. Finally, guidelines for possible efficient implementations, algorithm source code, and a library of reusable components are open-sourced to allow reproduction of our results and promote further investigations. [ABSTRACT FROM AUTHOR]

In this paper, a new approach for the formation of four‐member collaborative learning groups is presented. Group formation is presented by the mathematical optimization problem. Based on the proposed approach and the variable neighbourhood search (VNS) algorithm, the application that solves the presented problem and provides the appropriate division into groups is created. The proposed approach considers the scores of a pretest, interpersonal relationships, and prosocial behaviour/openness skill of students. In order to validate our approach, an experiment was designed with 108 first‐year university students of Belgrade Business School—Higher Educational Institution for Applied Studies. Experimental and control groups were divided into four‐member groups. The experimental group was divided by using the proposed method and the control group by student selection and random selection. Multilevel analysis is used to determine whether there is a significant difference in learning outcomes between the two groups. The experimental results showed that students from the experimental group achieved significantly higher success than the students from the control group. In addition, computational results obtained with the proposed VNS algorithms are compared and verified with the results obtained by random (Monte Carlo) method. Lay Description: What is currently known about the subject matter of this paper: Group formation have great influence on the success of collaborative learning.Consideration of multiple variables for group formation can be very demanding.Previous computer‐based methods for group formation do not use VNS. What this paper adds: In this paper, new metaheuristic approach for group formation is proposed.The proposed approach considers the scores of a pretest.The proposed approach considers interpersonal relationships.The proposed approach considers prosocial behaviour/openness skill of students. The implications of study findings for practitioners: The proposed approach have positive impact on students' academic performance.This approach can divide a large number of students into smaller groups based on multiple variables. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general solution approach for a broad class of vehicle routing problems that all use a single vehicle, composed of a truck and a detachable trailer, to serve a set of customers with known demand and accessibility constraints. A more general problem, called the extended single truck and trailer routing problem (XSTTRP), is used as a common baseline to describe and model this class of problems. In particular, the XSTTRP contains, all together, a variety of vertex types previously considered only separately: truck customers, vehicle customers with and without parking facilities, and parking-only locations. To solve the XSTTRP, we developed a fast and effective hybrid metaheuristic, consisting of an iterative core part, in which routes that define high-quality solutions are stored in a pool. Eventually, a set-partitioning-based postoptimization selects the best combination of routes that forms a feasible solution from the pool. The algorithm is tested on extensively studied problems from the literature, such as the multiple depot vehicle routing problem, the location routing problem, the single truck and trailer routing problem with satellite depots, and the single truck and trailer routing problem. Finally, computational results and a thorough analysis of the main algorithm's components on newly designed XSTTRP instances are provided. The obtained results show that the proposed hybrid metaheuristic is highly competitive with previous approaches designed to solve specific specialized problems, both in terms of computing time and solution quality. [ABSTRACT FROM AUTHOR]

New metaheuristic algorithms have soared over the past ten years. A common practice in proposing a new algorithm is validating it on several benchmark functions and engineering problems. Although CEC benchmark problems are specifically designed to validate the performance of new meta-heuristics, engineering design problems from pressure vessels to springs have been used in hundreds of papers to prove algorithm efficiency. To date, no benchmark practices have been established yet, i.e., researchers design their own benchmark to validate their algorithm. Thus, the high number of new algorithms combined with the high number of different benchmarking setups complicates the comparing and validating processes. In this paper, we study benchmark practices related to engineering applications. In particular, our exhaustive qualitative systematic review focuses on metaheuristics applied to the tension/compression spring design problem (TCSDP). The aim of this study is threefold: (i) evaluate where the field stands in regards of algorithm performance on the TCSDP, (ii) evaluate benchmarking practices, and (iii) facilitate future algorithm comparison. For these purposes, we first review all the existing metaheuristics applied to the TCSDP in their first publication. For each paper, we gather the data regarding the problem definition, the simulation setup, and the optimized design. We evaluated the data through several metrics to find the best-optimized design so far. Our findings and analysis concluded that the field of metaheuristics and its benchmarking practice have not reached maturity yet. Thus, we recommend some actions to address the issues and provide future research directions. [ABSTRACT FROM AUTHOR]

This paper deals with strip packing metaheuristic algorithm selection using data mining techniques. Given a set of solved strip packing problem instances, the relationship between the instance characteristics and algorithm performance is learned and is used to predict the best algorithms to solve a new set of unseen problem instances. A framework capable of modelling this relationship for an automated packing algorithm selection is proposed. The effectiveness of the proposed framework is evaluated in the context of a large set of strip packing problem instances and the state-of-the-art strip packing algorithms. The results suggest a 91% accuracy in correctly identifying the best algorithm for a given instance. [ABSTRACT FROM AUTHOR]

In this paper, we consider the contention aware task scheduling problem on a grid topology of processors. By contention awareness, we mean that simultaneous communication on a link has to be serialized. To solve this problem, we propose several nature inspired metaheuristic algorithms: Simulated Annealing (SA), Genetic Algorithm (GA), Differential Evolution (DE), Particle Swarm Optimization (PSO), Bat Algorithm (BA), Cuckoo Search (CS), and Firefly Algorithm (FA). We perform benchmark evaluation of these algorithms for the Normalized Schedule Length (NSL) parameter. The benchmark task graphs that we consider are: random task graphs, peer set task graphs, systolic array task graphs, Gaussian elimination task graphs, divide and conquer task graphs, and fast Fourier transform task graphs. [ABSTRACT FROM AUTHOR]

Due to several unique features, electrical discharge machining (EDM) has proved itself as one of the efficient non-traditional machining processes for generating intricate shape geometries on various advanced engineering materials in order to fulfill the requirement of the present day manufacturing industries. In this paper, the machining capability of an EDM process is studied during standard hole making operation on pearlitic SG iron 450/12 grade material, while considering gap voltage, peak current, cycle time and tool rotation as input parameters. On the other hand, material removal rate, surface roughness, tool wear rate, overcut and circularity error are treated as responses. Based on single- and multi-objective optimization models, this process is optimized using the teaching-learning-based optimization (TLBO) algorithm, and its performance is contrasted against firefly algorithm, differential evolution algorithm and cuckoo search algorithm. It is revealed that the TLBO algorithm supersedes the others with respect to accuracy and consistency of the derived optimal solutions, and computational efforts. [ABSTRACT FROM AUTHOR]

Agent-based metaheuristics computing paradigm (EMAS) has been proposed over 20 years ago by Cetnarowicz. Since then, many efforts were made in order to evaluate, formally analyze and further develop this paradigm towards creating new algorithms as EMAS hybrids, or EMAS-inspired techniques. However, at the same time a significant work has been done in order to build efficient software frameworks supporting this (and similar) computing paradigms. These frameworks were based not only on classic object-oriented programming, but also on functional approach and recently also utilizing heterogeneous infrastructure. This paper presents an overview of the most important findings in this area, including novel ways of processing the agents and component orientation, which allow for both high flexibility and high efficiency of provided solutions. The discussed concepts are illustrated with a case study of a system solving hard computational problem leveraging GPGPU. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the properties of the superior solution set search (SSSS) problem and point out the structural similarities between it and the multiobjective optimization problem. Based on the analyzed properties, we propose a new Firefly algorithm (FA) based on superior relations, which can search for the superior solution set by using the user's quantitative desire level as a search strategy. By introducing the distance of the problem space into the moving mechanism, FA makes it possible to search for multiple local optimal solutions by dividing the solution set into multiple groups. By analyzing this property of FA, we clarify the affinity between FA and the SSSS problem. We subsequently analyze the SSSS problem and FA, and discuss their properties together in a similar problem setting. We propose an FA based on superior relations as a new optimization technique for the superior solution set problem based on these analyses. Numerical experiments are then conducted using the SSSS problem and demonstrate the usefulness of the proposed method by comparing the performance of the proposed method with the conventional FA. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

• We introduce an RVRP where the last-mile delivery of some demands can be outsourced. • We propose construction and improvement heuristics handling outsourcing decisions. • The routes include the driving and rest periods according to European regulations. • We solve 60 artificial instances using our algorithms in classic metaheuristics. • The impact of the construction procedure and the outsourcing decisions are evaluated. This paper addresses a Rich Vehicle Routing Problem (RVRP) characterized by the following attributes: long-haul transport, driver hours regulation, incompatibility among goods, multiple depots and pickup locations, heterogeneous vehicles, time windows, and outsourcing decisions for last-mile delivery. Addressing the latter aspect is especially challenging, since it requires substantial changes in the algorithms for generating initial feasible solutions (construction heuristic) and for modifying existing solutions (improvement heuristics). Our work develops new heuristics adapted to the above attributes, and evaluates their performance in combination with common solving metaheuristics. We also assess the impact and the cost-effectiveness of the outsourcing attribute. [ABSTRACT FROM AUTHOR]

Metaheuristics, providing high level guidelines for heuristic optimisation, have successfully been applied to many complex problems over the past decades. However, their performances often vary depending on the choice of the initial settings for their parameters and operators along with the characteristics of the given problem instance handled. Hence, there is a growing interest into designing adaptive search methods that automate the selection of efficient operators and setting of their parameters during the search process. In this study, an adaptive binary parallel evolutionary algorithm, referred to as ABPEA, is introduced for solving the uncapacitated facility location problem which is proven to be an NP-hard optimisation problem. The approach uses a unary and two other binary operators. A reinforcement learning mechanism is used for assigning credits to operators considering their recent impact on generating improved solutions to the problem instance in hand. An operator is selected adaptively with a greedy policy for perturbing a solution. The performance of the proposed approach is evaluated on a set of well-known benchmark instances using ORLib and M*, and its scaling capacity by running it with different starting points on an increasing number of threads. Parameters are adjusted to derive the best configuration of three different rewarding schemes, which are instant, average and extreme. A performance comparison to the other state-of-the-art algorithms illustrates the superiority of ABPEA. Moreover, ABPEA provides up to a factor of 3.9 times acceleration when compared to the sequential algorithm based on a single-operator. • This paper proposes a multi-threaded adaptive evolutionary algorithm. • The proposed approach (ABPEA) is tested on the well-known binary-encoded problem UFLP. • An operator is selected adaptively with a greedy policy for perturbing a solution. • Three rewarding schemes, which are instant, average and extreme, are discussed. • Effect of varying the number of threads on the performance of ABPEA is investigated. [ABSTRACT FROM AUTHOR]

This paper proposes a fast ant colony system based solution method to solve realistic instances of the time-dependent orienteering problem with time windows within a few seconds of computation time. Orienteering problems occur in logistic situations where an optimal combination of locations needs to be selected and the routing between these selected locations needs to be optimized. For the time-dependent problem, the travel time between two locations depends on the departure time at the first location. The main contribution of this paper is the design of a fast and effective algorithm for this problem. Numerous experiments on realistic benchmark instances with varying size confirm the state-of-the-art performance and practical relevance of the algorithm. [ABSTRACT FROM AUTHOR]

Max-cut is one of the most classic NP-hard combinatorial optimization problems. The symmetry nature of it leads to special difficulty in extracting meaningful configuration information for learning; none of the state-of-the-art algorithms has employed any learning operators. This paper proposes an original learning method for max-cut, namely post-flip edge-state learning (PF-ESL). Different from previous algorithms, PF-ESL regards edge-states (cut or not cut) rather than vertex-positions as the critical information of a configuration, and extracts their statistics over a population for learning. It is based on following observations. 1) Edges are the only factors considered by the objective function. 2) Edge-states keep invariant when rotating a local configuration to its symmetry position, but vertex-positions do not. These suggest that edge-states contain more meaningful information about a configuration than vertex-positions do. It is impossible to set the state of an edge without influencing some other edges' states due to their dependencies. Therefore, instead of setting edge-states directly, PF-ESL samples the flips on vertices. Flips on vertices are sampled according to their capacities in increasing the similarity on edge-states between the given solution and a population. PF-ESL is employed in an EDA (Estimation of Distribution Algorithm) perturbation operator and a path-relinking operator. Experimental results show that our algorithm is competitive, and show that edge-state learning is value-added for both the two operators. The main contributions of this paper are as follows. Firstly, previous state-of-the-art evolutionary algorithms for max-cut focus on vertex positions in their evolutionary operation, this paper proposes a new and more reasonable perspective suggesting that edge-states are the critical information of divided graphs rather than vertex positions, and introduces a novel method to measure and utilize their similarities based on it. Such a perspective is fundamental to learning based algorithms design for max-cut and other graph partitioning problems, and can shed lights on future researches. Furthermore, since max-cut is one of the most classic and fundamental NP hard problems, many real-world problems involve dividing graph data into different parts to optimize certain functions, this new perspective may inspire related or similar problems. Secondly, besides the original edge-states based perspective, and the post-flip edge-states learning (PFESL) operator based on it, our memetic algorithm also incorporates a novel evolutionary framework which alternates between EDA based Iterated Tabu search (ITS) and path relinking based genetic algorithm. Finally, the proposed algorithm provides competitive results on two mostly used benchmark sets and improves the best-known results of 6 most challenging instances. • An original edge-state perspective for design learning operators for max-cut. • A novel learning operator to learn edge states. • A new evolutionary framework for max-cut. • It provides competitive results on two mostly used benchmark sets. [ABSTRACT FROM AUTHOR]

This paper proposes a novel population based optimization algorithm called Andean Condor Algorithm (ACA) for solving cell formation problems. The ACA metaheuristic is inspired by the movement pattern of the Andean Condor when it searches for food. This pattern of movement corresponds to the flight distance traveled by the Andean Condor from its nest to the place where food is found. This distance varies depending on the seasons of the year. The ACA metaheuristic presents a balance of its population through a performance indicator based on the average quality of the population's fitness. This balance determines the number of Andean Condors that will perform an exploration or intensification movements. ACA metaheuristics have a flexible design. It allows to easily integrate specific heuristics according to the optimization problem to be solved. Two types of computational experiments have been performed. According to the results obtained it has been possible to determine that ACA is an algorithm with an outstanding RPD% in relation to the algorithms BAT, MBO and PSO, robust and with a convergence which tends not to be trapped in the local optimums. Besides, according to the non-parametric multiple comparison, results have been obtained in which the ACA metaheuristic has significant differences in relation to the BAT, MBO and PSO algorithms. [ABSTRACT FROM AUTHOR]